Problem 3

Police car is chasing a speed limit violator car with aDoppler radar installed on the roof. Suppose the speed of sound is300 m/s. When the police car has a velocity v = 10 m/s in the labframe, it sends a 30 kHz frequency signal.

3.1 If the violator is moving at 20 m/s, what would bethe frequency of the radar signal if received by an instrumentinstalled at the violator car?

3.2 If the police car detected a returning signal at 29kHz (after bouncing off the violator’s car), what is the velocityof the violator? Describe the situation in words.

Suppose we took a parallel plates capacitor: the plateshave area 1 by 1 meter and they are separated by 1 cm withvacuum.

3.3 What would be the force between the two plates if wedeposit a charge of 1 Coulomb.

3.4 How will the force in 3.3 change if we fill thespace between the capacitors plate with a silicon, which has adielectric relative permittivity of 10.

Suppose we have made a different capacitor, whichconsists of two oppositely charged small spheres with a radius Rseparated by a distance D. Assume R << D and the charge isdistributed uniformly on the surface of the sphere. Consider anX-axis originating in the center of the first sphere and goingthrough the center of the second sphere. The two centers are at X =0 and X =D.

3.5 Sketch the electric field between X = R and X =D-R.

3.6 If once the sphere is given a charge Q and the other–Q, calculate the voltage difference between the twospheres.

3.7 Calculate the capacitance and express it via R, D,and epsilon_0.